The most important goal of this paper is to enhance our understanding of the crucial functional relationships that determine the behavior of the systemic circulation and its underlying physiological regulatory mechanisms with minimal modeling. To the present day, much has been said about the indirect hydraulic effects of right atrial pressure (Pra) via cardiac output (CO) on arterial pressure (Pa) through the heart and pulmonary circulation or the direct regulatory effects of Pra on Pa through the cardiopulmonary baroreflex; however, very little attention has been given to the hydraulic influence that Pra exerts directly through the systemic circulation. The experimental data reported by Guyton et al in 1957 demonstrated that steadystate Pra and the rate at which blood passes through the systemic circulation are locked in a functional relationship independent of any consequence of altered Pra on cardiac function. With this in mind, we emphasize the analytic algebraic analysis of the systemic circulation composed of arteries, veins and its underlying physiological regulatory mechanisms of baroreflex and autoregulatory modulation of total peripheral resistance (TPR), where the behavior of the system can be analytically synthesized from an understanding of its minimal elements. As a result of this analysis, we present a novel mathematical method to determine short-term TPR fluctuations, which accounts for the entirety of observed Pa fluctuations, and propose a new cardiovascular system identification method to delineate the actual actions of the physiological mechanisms responsible for the dynamic couplings between CO, Pa, Pra and TPR in an individual subject.